§1.2 White dwarves and novae

White dwarf matter is so highly compressed that a bowling ball filled with the stuff would tip the scales at over a thousand tons–about the weight of a small ocean liner.

In normal stars, the relationship between pressure, density and temperature is well-described by the ideal gas law [Rolfs and Rodney 1988]. This relationship holds as long as nuclear fuel remains to provide heat and energy. Once the fuel runs out, however, the star no longer is able to support itself, and its material then collapses.

Chandrasekhar showed that if the remaining mass is less than 1.4 solar masses, the object may be supported from further collapse by electrons behaving as a Fermi gas [Chandrasekhar 1939]. The electrons in a star are the most numerous particles, especially in a white dwarf. White dwarves are primarily ashes from the later stages of nuclear burning, such as carbon, oxygen, neon and magnesium.

As fermions, electrons are governed by the Pauli exclusion principle, which says that no two identical fermions may inhabit the same quantum state. In a white dwarf, the electrons have filled up all available quantum states up to the Fermi energy. A solar mass white dwarf has a radius of approximately 8000 km (only slightly higher than the earth), making these objects very dense (~10⁶ g⋅cm^-3) [Rolfs and Rodney 1988].

When it is in a close binary system with an actively burning star, the dwarf’s strong gravitational field will gradually pull material onto its surface from the less dense star. The falling matter also heats up the surface with the kinetic energy it gains. A normal star would expand as it heats up, lowering the density. The degeneracy (i.e., T∕T_F≪1) of the white dwarf [Pathria 1996] prevents this, however. Thermonuclear runaway may occur if the temperature dependence of nuclear energy generation exceeds the temperature dependence of energy loss through cooling [Weischer Görres et al. 1999].

Periodically, the heating will bring the surface material to a sufficient temperature for explosive nuclear burning to occur, that is, condition (1.6) is satisfied. (If the mass accretion is fast enough, such as with a red giant partner, the explosion may be violent enough to completely disperse the dwarf. These events are know as Type Ia supernovae [Rolfs and Rodney 1988].)

The burning layers generate energy at such a large rate that they expand rapidly, i.e., the surface layers are not degenerate like the bulk of the white dwarf. The burning continues as long as the expansion hasn’t reduced the temperature and density too far. The peak of visible light observed by astronomers actually occurs during this expansion and cooling phase, because the luminosity of a radiating object is proportional to its surface area. Of particular interest in this study is the gamma-ray flux potentially observable from such objects.

Table 1 shows the proton-rich radioactive nuclei that may contribute significantly to observable γ-rays from novae [Hernanz, José et al. 1999]. Any left over nuclei on the proton rich side of the valley of β-stability may be sources of 511-keV γ-radiation, but ¹⁸F and ²²Na are thought to dominate the 511-keV flux. The waiting point nucleus, ¹³N, has a lifetime so short that it has mostly decayed before the expanding matter becomes transparent to γ-rays. The ²²Na is present only in oxygen-neon novae and its long lifetime relative to ¹⁸F makes its 511-keV emission weaker; however, its daughter, ²²Ne, emits a unique 1275-keV γ-ray which may eventually be observable [Clayton and Hoyle 1974]. ¹⁸F, which decays directly to the ground state of ¹⁸O, has a 2.6-hour lifetime, allowing it to be strongly observable if it is produced in sufficient quantities. The effect of ¹⁸F+p resonances in ¹⁹Ne on ¹⁸F production in novae is one of the subjects of this thesis.